The invention relates to a method of plotting surfaces in a volume with three dimensions X, Y, Z, enabling the use of two-dimensional algorithms. Applied to seismology, this method enables in particular the reliable, semi-automatic mapping of seismic horizons in a region in which a 3D-recording program has been carried out and thus constitutes a valuable aid in the structural and stratigraphic interpretation of this region, for better oil exploration.
In many fields, there is a need to display and/or explore information contained in a volume. The great majority of techniques for exploration of such a volume of data consists in linearising so that the exploration of such a volume is carried out by way of the exploration of a set of planes or a set of complementary lines the union of which constitutes the volume.
Several linearisation techniques are known enabling the passage from an N-dimensional space to a space of lower dimension. Thus, the TV-scanning technique commonly used in the field of telecommunications or for tomography for example, enables the line-by-line description of a picture with two dimensions X, Y which is composed of a set of lines for which X is variable and Y constant.
In oil prospecting, geophysicists use a particular technique called "reflection seismology" which consists in emitting acoustic signals at ground level and in recording them after the said signals have been reflected at the borders between the various superimposed geological layers constituting the sub-soil and the topography of which it is desired to reconstruct. Two method-of acquiring these seismic recordings are mainly used. The first, a conventional method, consists in distributing emitters and receivers over a same surface line of X coordinates. This 2-dimensional method of acquisition enables a particular picture of the sub-soil, referred to as the seismic section, to be obtained, and which can be likened to a vertical cross-sectional plane of the sub-soil along the acquisition line, on which the borders between geological layers appear as sub-horizontal lineations. Each section consists of a succession of recordings sampled as a function of time or of depth Z, each representing the vertical situated directly below a point Pi with known coordinate Xi varying uniformly from one recording to the next. The exploration of these sections consists in carrying out a manual or automatic plotting of the various lineations.
The second method, up to now reserved essentially for studies of deposits presenting a structural problem, consists in distributing at ground level emitters and receivers distributed over a grid of coordinates X, Y in a horizontal plane. This type of acquisition, referred to as "3D acquisition", enables a three-dimensional picture of the sub-soil to be obtained, which picture consists of recordings sampled as a function of time or of depth Z, each representing the vertical directly below a point Pij with coordinates Xi, Yj varying uniformly from one recording to the next. To explore such a volume of 3D data, it has always been desired, in seismology, to reduce this to a conventional 2D-type acquisition so as to be able to use plotting or other tools and procedures developed for 2D-section exploration.
It is therefore considered that each 3D consists of a succession of parallel lines each associated with a constant Y, and which can be explored as an equal number of elementary 2D sections. The conventional interpretation of a 3D acquisition consists in carrying out a manual plotting of certain seismic horizons, in taking the times or depth of these horizons directly below each line and in mapping these horizons in horizontal cross-sectional planes with coordinates X, Y. There exist tools for so-called "automatic surface plotting of 3D horizons", such as "SPACE TRACK".RTM. developed by GSI, necessitating an interpretation post consisting of at least one microcomputer with memory and display screen. The tools enable the virtually instantaneous representation, from a volume of data stored in memory, of the seismic horizon surfaces manually plotted and digitised beforehand on the elementary 2D sections constituting the 3D acquisition. The use of tools for automatic plotting necessitates the linearisation of the 3D volume. The linearisations carried out up to now consist in juxtaposing the successive planes so as to obtain a seismic section of length equal to the sum of the lengths of the elementary sections constituting the data volume. Such a technique inspired by the scanning technique has the disadvantage in seismology that it introduces, on each passage from one plane to the next, a discontinuity which is manifested by a phase shift, which may be large, between the pictures of a same horizon. Now, the programs used for the exploration of seismic sections are very sensitive to phase shifts, in particular the reflector plotting programs which do not give satisfactory results in this case. The use of an inverted scanning technique consisting in describing each plane in a sense inverse to the previous one, enables discontinuities to be avoided, but introduces cusps at the uneven borders of planes to which the programs for interpretation, in particular for plotting, are also sensitive.
Another disadvantage of these techniques employed resides in the fact that the concept of neighbourhood does not exist insofar as the information relating to a given vertical is very distant, after linearisation, from the information relating to a vertical neighbouring the previous one but situated in a different plane. Taking account of the local context under these conditions is not possible, which can be very awkward if the result of the exploration of the data volume depends on regionally varying characteristics.